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Linear Stability Analysis of Solitons Governed by the 2D Complex Cubic-Quintic Ginzburg-Landau Equation 二维复三次-五次金兹堡-朗道方程控制孤子的线性稳定性分析
SIAM undergraduate research online Pub Date : 2023-01-01 DOI: 10.1137/23s1548116
Emily Gottry
{"title":"Linear Stability Analysis of Solitons Governed by the 2D Complex Cubic-Quintic Ginzburg-Landau Equation","authors":"Emily Gottry","doi":"10.1137/23s1548116","DOIUrl":"https://doi.org/10.1137/23s1548116","url":null,"abstract":". We used the singular value decomposition to construct a low-dimensional model that qualitatively describes the behavior and dynamics of optical solitons governed by the complex cubic-quintic Ginzburg-Landau equation in two spatial dimensions. With this model, it was found that a single soliton destabilizes and transitions into a double-soliton configuration through an intermediate periodic phase as the gain increases. Linear stability analysis then revealed that a Hopf bifurcation occurs at several critical gain values corresponding to the destabilization of the single and double solitons.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64318103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ride Like the Wind Without Getting Winded: The Growth of E-Bike Use 像风一样骑行而不气喘:电动自行车使用的增长
SIAM undergraduate research online Pub Date : 2023-01-01 DOI: 10.1137/23s1577213
Jerry Sheng
{"title":"Ride Like the Wind Without Getting Winded: The Growth of E-Bike Use","authors":"Jerry Sheng","doi":"10.1137/23s1577213","DOIUrl":"https://doi.org/10.1137/23s1577213","url":null,"abstract":"","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64318227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Comparison of Vector Voting Rules and Their Relation to Simple Majority Voting 向量投票规则的比较及其与简单多数投票的关系
SIAM undergraduate research online Pub Date : 2023-01-01 DOI: 10.1137/22s1536418
Zhuorong Mao
{"title":"Comparison of Vector Voting Rules and Their Relation to Simple Majority Voting","authors":"Zhuorong Mao","doi":"10.1137/22s1536418","DOIUrl":"https://doi.org/10.1137/22s1536418","url":null,"abstract":"Introduced here are examples of what we call “vector voting rules” : social preference orderings deduced from vectors naturally associated with the group preference matrix. These include higher-order Borda Rules , B p , p = 1, 2, ..., and the Perron Rule (P). We study the properties of these transitive rules and compare them with Simple Majority Voting (SMV). Even when SMV is transitive, it can yield results different from B 1 , B 2 , ... and P, and through simulation, we compile statistics about how often these differ. We also give a new condition ( 2/3+ majorities ) that is (just) sufficient for SMV to be transitive and then quantify the frequency of transitivity for graded failures of this hypothesis.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64317561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantifying Uncertainty in Ensemble Deep Learning 集成深度学习中不确定性的量化
SIAM undergraduate research online Pub Date : 2023-01-01 DOI: 10.1137/22s1531816
Emily Diegel, Rhiannon Hicks, Max Prilutsky, R. Swan
{"title":"Quantifying Uncertainty in Ensemble Deep Learning","authors":"Emily Diegel, Rhiannon Hicks, Max Prilutsky, R. Swan","doi":"10.1137/22s1531816","DOIUrl":"https://doi.org/10.1137/22s1531816","url":null,"abstract":"Neural networks are an emerging topic in the data science industry due to their high versatility and efficiency with large data sets. Past research has utilized machine learning on experimental data in the material sciences and chemistry field to predict properties of metal oxides. Neural networks can determine underlying optical properties in complex images of metal oxides and capture essential features which are unrecognizable by observation. However, neural networks are often referred to as a “black box algorithm” due to the underlying process during the training of the model. This poses a concern on how robust and reliable the prediction model actually is. To solve this ensemble neural networks were created. By utilizing multiple networks instead of one the robustness of the model was increased and points of uncertainty were identified. Overall, ensemble neural networks outperform singular networks and demonstrate areas of uncertainty and robustness in the model.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64317599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Iterative Methods at Lower Precision 低精度迭代方法
SIAM undergraduate research online Pub Date : 2023-01-01 DOI: 10.1137/22s152637x
Xiang Ji, Xiaoyun Gong, Yizhou Chen
{"title":"Iterative Methods at Lower Precision","authors":"Xiang Ji, Xiaoyun Gong, Yizhou Chen","doi":"10.1137/22s152637x","DOIUrl":"https://doi.org/10.1137/22s152637x","url":null,"abstract":"","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135783391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Food Deserts and k-Means Clustering 食物沙漠和k-均值聚类
SIAM undergraduate research online Pub Date : 2023-01-01 DOI: 10.1137/22s1504445
Garrett Kepler
{"title":"Food Deserts and k-Means Clustering","authors":"Garrett Kepler","doi":"10.1137/22s1504445","DOIUrl":"https://doi.org/10.1137/22s1504445","url":null,"abstract":". Food deserts are regions where people lack access to healthy foods. In this article we use k-means clustering to cluster the food deserts in two Bay Area counties. The centroids (means) of these clusters are optimal locations for intervention sites (such as food pantries) since they minimize the distance that a person within a food desert cluster would need to travel to reach the resources they require. We present the results of both a standard and a weighted k-means clustering algorithm. The weighted algorithm takes into account the poverty levels in each food desert when determining the placement of a centroid. We find that this weighting can make significant changes to the proposed locations of intervention sites.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64317197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Maximizing Harvest Yields in a Three-Species System 三种系统中收获产量最大化
SIAM undergraduate research online Pub Date : 2023-01-01 DOI: 10.1137/23s1546737
Jacob Kahn
{"title":"Maximizing Harvest Yields in a Three-Species System","authors":"Jacob Kahn","doi":"10.1137/23s1546737","DOIUrl":"https://doi.org/10.1137/23s1546737","url":null,"abstract":"Management decisions on sustainable harvesting of any species in our marine ecosystems benefit from mathematical modeling and simulations due to the underlying complex ecological interactions between species. Using basic mathematical analysis and numerical simulation tools, we consider the problem of investigating the maximum sustainable yield (MSY) and the maximum economic yield (MEY) when harvesting in a fishery system consisting of one predator and two competing prey species. Results show that the harvesting effort required to achieve MEY is less than what is needed to achieve MSY. This implies that increasing harvesting effort beyond what is needed to reach MEY will not necessarily deliver more profits but may run the risk of driving some of the species of the system into extinction. Furthermore, results show that under the MEY management policy, a predator-oriented harvesting approach is recommended when harvesting single-species only. For double-species harvesting in a system with weak interspecific competition and weak predation, a prey-oriented harvesting approach is recommended, but when there is strong interspecific competition and strong predation, a predator-oriented harvesting approach is recommended.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136002853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multi-scale Hybridized Topic Modeling: A Pipeline for Analyzing Unstructured Text Datasets via Topic Modeling 多尺度杂交主题建模:一种基于主题建模的非结构化文本数据分析管道
SIAM undergraduate research online Pub Date : 2022-11-24 DOI: 10.1137/22s1536832
Keyi Cheng, Stefan Inzer, Adrian Leung, Xiaoxian Shen, Michael Perlmutter, Michael Lindstrom, Joyce A. Chew, Todd Presner, D. Needell
{"title":"Multi-scale Hybridized Topic Modeling: A Pipeline for Analyzing Unstructured Text Datasets via Topic Modeling","authors":"Keyi Cheng, Stefan Inzer, Adrian Leung, Xiaoxian Shen, Michael Perlmutter, Michael Lindstrom, Joyce A. Chew, Todd Presner, D. Needell","doi":"10.1137/22s1536832","DOIUrl":"https://doi.org/10.1137/22s1536832","url":null,"abstract":"We propose a multi-scale hybridized topic modeling method to find hidden topics from transcribed interviews more accurately and efficiently than traditional topic modeling methods. Our multi-scale hybridized topic modeling method (MSHTM) approaches data at different scales and performs topic modeling in a hierarchical way utilizing first a classical method, Nonnegative Matrix Factorization, and then a transformer-based method, BERTopic. It harnesses the strengths of both NMF and BERTopic. Our method can help researchers and the public better extract and interpret the interview information. Additionally, it provides insights for new indexing systems based on the topic level. We then deploy our method on real-world interview transcripts and find promising results.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47735325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Adapting Zeroth Order Algorithms for Comparison-Based Optimization 基于比较优化的零阶自适应算法
SIAM undergraduate research online Pub Date : 2022-10-11 DOI: 10.1137/22s1530951
Isha Slavin, Daniel Mckenzie
{"title":"Adapting Zeroth Order Algorithms for Comparison-Based Optimization","authors":"Isha Slavin, Daniel Mckenzie","doi":"10.1137/22s1530951","DOIUrl":"https://doi.org/10.1137/22s1530951","url":null,"abstract":"Comparison-Based Optimization (CBO) is an optimization paradigm that assumes only very limited access to the objective function f(x). Despite the growing relevance of CBO to real-world applications, this field has received little attention as compared to the adjacent field of Zeroth-Order Optimization (ZOO). In this work we propose a relatively simple method for converting ZOO algorithms to CBO algorithms, thus greatly enlarging the pool of known algorithms for CBO. Via PyCUTEst, we benchmarked these algorithms against a suite of unconstrained problems. We then used hyperparameter tuning to determine optimal values of the parameters of certain algorithms, and utilized visualization tools such as heat maps and line graphs for purposes of interpretation. All our code is available at https://github.com/ishaslavin/Comparison_Based_Optimization.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47937063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A Quasi-Optimal Spectral Solver for the Heat and Poisson Equations in a Closed Cylinder 封闭圆柱中热和泊松方程的拟最优谱解算器
SIAM undergraduate research online Pub Date : 2022-06-10 DOI: 10.1137/22s1502070
David Darrow
{"title":"A Quasi-Optimal Spectral Solver for the Heat and Poisson Equations in a Closed Cylinder","authors":"David Darrow","doi":"10.1137/22s1502070","DOIUrl":"https://doi.org/10.1137/22s1502070","url":null,"abstract":"We develop a spectral method to solve the heat equation in a closed cylinder, achieving a quasi-optimal $mathcal{O}(Nlog N)$ complexity and high-order, spectral accuracy. The algorithm relies on a Chebyshev--Chebyshev--Fourier (CCF) discretization of the cylinder, which is easily implemented and decouples the heat equation into a collection of smaller, sparse Sylvester equations. In turn, each of these equations is solved using the alternating direction implicit (ADI) method in quasi-optimal time; overall, this represents an improvement in the heat equation solver from $mathcal{O}(N^{4/3})$ (in previous Chebyshev-based methods) to $mathcal{O}(Nlog N)$. While Legendre-based methods have recently been developed to achieve similar computation times, our Chebyshev discretization allows for far faster coefficient transforms; we demonstrate the application of this by outlining a spectral method to solve the incompressible Navier--Stokes equations in the cylinder in quasi-optimal time. Lastly, we provide numerical simulations of the heat equation, demonstrating significant speed-ups over traditional spectral collocation methods and finite difference methods.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49609379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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